186 Mr. W. Ferrel on a controverted Point in 



K 4 =0 would give direct instead of inverted tides at the equa- 

 tor. With this depth we should have in the case of the canals 

 the tides inverted between the parallels of 22°, and all between 

 these parallels and the poles would be direct ones. If we 

 now suppose the partitions between the canals to be removed, 

 it is reasonable to suppose that the predominating direct tides 

 over the greater part of the globe, by means of the interchang- 

 ing motions between the different latitudes, would reverse the 

 tides at the equator, and hence that this reversal would occur 

 with about this depth of the sea, as my tidal expression with 

 K 4 =0 gives it, and not at a depth of about 3*5 miles, as given 

 by Laplace's values of K 4 . 



Of course this comparison of the results obtained with 

 Laplace's value of K 4 and with K 4 = with those given by 

 the canals does not amount to a demonstration ; but it makes 

 the results obtained with K 4 = so probable and those obtained 

 with Laplace's values so extremely improbable, that we should 

 hesitate in accepting the latter without a very critical exami- 

 nation of all the principles and processes upon which they are 

 based. 



We now come to Sir William Thomson's second paper, in 

 the October Number of the Philosophical Magazine, p. 279. 

 In this, it is seen, he adds a constant B to the expression of 

 a', as assumed by Airy and adopted by myself; and the expres- 

 sion thus becomes 



a'=B + B 2 ^ 2 + B 4/ x 4 + ... 



This constant is properly added and supplies a deficiency in 

 the expression as first assumed by Airy, it being one of the 

 two implied arbitrary constants in the solution of a differen- 

 tial equation of the second degree, which, it will be shown, 

 cannot in this case vanish. Retaining this constant and car- 

 rying out the solution as usual by determining the other con- 

 stants by means of the equations (5) and (6) given by Sir 

 William Thomson, we get 



B 2 =0, 



B 4 =Z(B + H), 



B 6 =§ZB , 



B 8 =i^ + 1 y 2 (B + H), 



B l0 =fZB + ^Z 2 B + ^Z 2 (B + H), 



With these values of these constants the expression of a' 

 contains the arbitrary constant B , which remains to be yet 

 determined. But this constant cannot be determined by any 

 condition obtained from within the differential equation itself, 



